Treewidth and Minimum Fill-in of Weakly Triangulated Graphs

@inproceedings{Bouchitt1999TreewidthAM,
  title={Treewidth and Minimum Fill-in of Weakly Triangulated Graphs},
  author={Vincent Bouchitt{\'e} and Ioan Todinca},
  booktitle={STACS},
  year={1999}
}
We use the notion of potential maximal clique to characterize the maximal cliques appearing in minimal triangulations of a graph. We show that if these objects can be listed in polynomial time for a class of graphs, the treewidth and the minimum fill-in are polynomially tractable for these graphs. Finally we show how to compute in polynomial time the potential maximal cliques of weakly triangulated graphs. 
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